The swallowtail integral in the highly oscillatory region III

Ferreira, C. (Universidad de Zaragoza) ; López, J.L. ; Pérez Sinusía, E. (Universidad de Zaragoza)

Resumen: We consider the swallowtail integral (Formula presented.) for large values of (Formula presented.) and bounded values of (Formula presented.) and (Formula presented.). The integrand of the swallowtail integral oscillates wildly in this region and the asymptotic analysis is subtle. The standard saddle point method is complicated and then we use the modified saddle point method introduced in López et al., A systematization of the saddle point method application to the Airy and Hankel functions. J Math Anal Appl. 2009;354:347–359. The analysis is more straightforward with this method and it is possible to derive complete asymptotic expansions of (Formula presented.) for large (Formula presented.) and fixed x and y. The asymptotic analysis requires the study of three different regions for (Formula presented.) separated by three Stokes lines in the sector (Formula presented.). The asymptotic approximation is a certain combination of two asymptotic series whose terms are elementary functions of x, y and z. They are given in terms of an asymptotic sequence of the order (Formula presented.) when (Formula presented.), and it is multiplied by an exponential factor that behaves differently in the three mentioned sectors. The accuracy and the asymptotic character of the approximations are illustrated with some numerical experiments.

Idioma: Inglés

DOI: 10.1080/17476933.2020.1868447

Año: 2022

Publicado en: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 67, 5 (2022), 1262-1272
ISSN: 1747-6933

Factor impacto JCR: 0.9 (2022)

Categ. JCR: MATHEMATICS rank: 147 / 329 = 0.447 (2022) - Q2 - T2

Factor impacto CITESCORE: 1.8 - Mathematics (Q3)

Factor impacto SCIMAGO: 0.457 - Analysis (Q2) - Applied Mathematics (Q2) - Computational Mathematics (Q3) - Numerical Analysis (Q3)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)